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A068019
Composite n such that both 1 + phi(n) and -1 + phi(n) are primes, i.e., phi(n) is the middle term between twin primes (A014574).
4
8, 9, 10, 12, 14, 18, 21, 26, 27, 28, 36, 38, 42, 49, 54, 62, 77, 86, 91, 93, 95, 98, 99, 111, 117, 122, 124, 133, 135, 146, 148, 152, 154, 171, 182, 186, 189, 190, 198, 206, 209, 216, 217, 218, 221, 222, 228, 234, 252, 266, 270, 278, 279, 287, 291, 297, 302
OFFSET
1,1
COMMENTS
A072281 with the primes removed; intersection of A066071 and A078893. - Ray Chandler, May 26 2008
LINKS
EXAMPLE
n = 21, 26, 28, 36, 42 give phi(n)=12; the corresponding twin primes are {11,13}.
MATHEMATICA
Do[s=-1+EulerPhi[n]; s1=1+EulerPhi[n]; If[PrimeQ[s]&&PrimeQ[s1]&&!PrimeQ[n], Print[n]], {n, 1, 2000}]
(* Second program: *)
Select[Range[4, 302], And[CompositeQ@ #, AllTrue[EulerPhi@ # + {-1, 1}, PrimeQ]] &] (* Michael De Vlieger, Dec 08 2018 *)
PROG
(PARI) isok(n) = !isprime(n) && isprime(eulerphi(n)+1) && isprime(eulerphi(n)-1); \\ Michel Marcus, Dec 08 2018
(GAP) Filtered([1..310], n->not IsPrime(n) and IsPrime(1+Phi(n)) and IsPrime(-1+Phi(n))); # Muniru A Asiru, Dec 08 2018
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 08 2002
STATUS
approved